Question: ${\sqrt[3]{1458} = \text{?}}$
$\sqrt[3]{1458}$ is the number that, when multiplied by itself three times, equals $1458$ First break down $1458$ into its prime factorization and look for factors that appear three times. So the prime factorization of $1458$ is $2\times 3\times 3\times 3\times 3\times 3\times 3$ Notice that we can rearrange the factors like so: $1458 = 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = (3\times 3\times 3) \times (3\times 3\times 3) \times 2$ So $\sqrt[3]{1458} = \sqrt[3]{3\times 3\times 3} \times \sqrt[3]{3\times 3\times 3} \times \sqrt[3]{2}$ $\sqrt[3]{1458} = 3\times 3 \times \sqrt[3]{2}$ $\sqrt[3]{1458} = 9 \sqrt[3]{2}$